本项目主要研究微分分次模的同调维数及微分分次范畴的recollements和Morita理论。通过对dg模同调维数的性质及相互间关系的刻画，试图在更一般dg代数上研究dg模的amplitude不等式、导出深度公式、导出宽度公式、Auslander-Buchsbaum公式和Bass公式成立的条件；寻找三个dg代数的导出范畴间recollement存在的判断准则，试图构造dg代数的同伦范畴和导出范畴间的各种recollements，进而建立dg代数的有限维数和整体维数间的相互关系；利用模型结构理论进一步研究dg范畴中的Morita理论，讨论两个dg代数的有界(无界)导出范畴和同伦范畴的三角等价，讨论两个dg代数谱的模范畴作为模型范畴的Quillen等价。本研究将丰富和发展dg模的同调维数理论及其导出范畴的recollement和Morita理论，以推动代数学及其它学科的进一步发展。

The main object of project is to study the homological dimensions of differential graded modules, recollements and Morita theory of differential graded categories. Through the characterization of various homological dimensions of dg modules and the relations between them, we will establish amplitude inequality, derived depth formula, derived width formula, Auslander-Buchsbaum formula and Bass formula of dg modules on more general dg algebras; search the judgment criterion for the existence of recollement in the derived category of three dg algebras; attempts to construct various recollements of homotopy categories and derived categories of dg algebras, and then establishes the relation between finite dimension and global dimension of dg algebras; further study Morita theory of dg category by using model structure theory, discuss the equivalence of bounded (unbounded) derived categories and homotopy categories of two dg algebras, and Quillen equivalence of the categories of modules of two dg algebras spectrum. The study of this project will enrich and develop the homological dimension theory of dg modules, recollements and Morita theory of homotopy categories and derived categories, and further promote the development of algebra and other subjects.